Home Depot sells mole smoke bombs that gas them to death. They smell like hell (so close all the windows in your house) but they work pretty well if you find an active tunnel.

Funny story, I was Turkey Hunting on some private property up the Teanaway. The old boy who owned the land had the best mole trap ever. It was a 20 ga shotgun strapped barrel facing down on an old pull golf cady. The trigger was hooked to a wire that ran down into the hole with some bait attached. When the mole pulled on the bait it was blasted with some #7s. Not safe around kids but effective on varmints.

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I use that stuff, but there's a lot of "replacement moles" around my place that keep moving in. Its not safe for humans to breath the fumes either, so quickly deploy the bomb as directed, fuse-first into the hole, hold your breath before it starts going off, instantly cover the hole with a short block of 2x4, then cover that with dirt...all of this as quickly as possible, trying to not let any of the gas escape.

I have a spring-powered spike trap, but I need to make the trigger release more sensitive. So far the factory setting is too tight, and the dang thing hasn't worked.
I have an electronic mole repeller, and that works until the moles finally get used to it.
I'm going to try the wriggly's gum.
Once, I was able to spear one that was pushing up dirt (caught in the act!) with a home-made mole spear. It was a long-bladed carving knife taped to a broom handle.

Cats are useless against moles. I did see the neighbor's aggro Pit Bull dig up a mole and bite it to death. Made my day! the dog got a little too aggro and also bit another neighbor's dog to death, and had to be put to sleep. RIP Belle, I miss ya!

The juicy fruit gum suggestion gave me an idea that might work. Roll up a stick of pink colored gum and work it like a chunk of epoxy putty until its soft enough to shape into the form of a worm.
Place it in a mole hole and recite the following words: "Here ya go! I brought a nice treat for my little buddy! A fat pink worm! Just for you!"

Then, as you walk away, mutter under your breath: "I hope you choke on it, you little ratf*#*er!"

Of course, moles are a lot smarter than steelhead, and this might not work as well as one hopes.

I had a cat that cleared our mole problem out within a month back in Nebraska. My cats now just bring live moles into the apartment.

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You are lucky. The moles in my yard build tunnels anywhere from 4" to over a foot underground. The neighbor's cats just poop on the mole hills, but are too lazy to dig after the moles. They like to hunt songbirds, instead.

With this rain, several new mole hills have appeared in my yard, and this morning it looks like a whole team of them are invading from the overgrown empty lot next door.

I have concrete walkways and a patio that the moles burrow under, and they create large piles on the edges. I finally figured out how to kill the ones living there:
I opened a tunnel on one end of my patio, and another on the opposite end that was in-line with another mound that was near to it, but out away from the edge of my patio. I opened the nearby mound. Now I had three open holes.
I duct-taped a hose extension to my leaf blower and inserted the hose end into the outer hole, and sealed it with dirt. Now I had a blower system ready to go on one end of the tunnel system. I deployed the gas bomb in the middle hole (next to the blower) and quickly covered it up, then turned on my blower. When I saw the fumes coming out of the far hole, I shut off the blower and sealed the far hole.

I did this in a couple other spots, too.
That killed the moles, but there seem to be an infinite number of reinforcements ready to invade from the outer perimeters. I suppose that one must have something to fight. My area is unincorporated, and there's no "city hall."

You are lucky. The moles in my yard build tunnels anywhere from 4" to over a foot underground. The neighbor's cats just poop on the mole hills, but are too lazy to dig after the moles. They like to hunt songbirds, instead.

With this rain, several new mole hills have appeared in my yard, and this morning it looks like a whole team of them are invading from the overgrown empty lot next door.

I have concrete walkways and a patio that the moles burrow under, and they create large piles on the edges. I finally figured out how to kill the ones living there:
I opened a tunnel on one end of my patio, and another on the opposite end that was in-line with another mound that was near to it, but out away from the edge of my patio. I opened the nearby mound. Now I had three open holes.
I duct-taped a hose extension to my leaf blower and inserted the hose end into the outer hole, and sealed it with dirt. Now I had a blower system ready to go on one end of the tunnel system. I deployed the gas bomb in the middle hole (next to the blower) and quickly covered it up, then turned on my blower. When I saw the fumes coming out of the far hole, I shut off the blower and sealed the far hole.

I did this in a couple other spots, too.
That killed the moles, but there seem to be an infinite number of reinforcements ready to invade from the outer perimeters. I suppose that one must have something to fight. My area is unincorporated, and there's no "city hall."